

/ LI.VKS 



from the or: instance is called the intercept of 



til-- plane on the axis. If a, 6, c be the intercepts on the JS 

 .-axes, respectively, of the plane whose equation is 

 1 / + By + d + D - 0, 



tli -n tli. ja'int^ i,0,0). ), (0, 0, e) are points of the 



Cc + /> - 0, 



Aa + D - 0, Bb + D - 0, 



Hence equation (1) may be written 



and this is the equation of the plane in terms of its intercepts. 



217. The normal equation of a plane. A plane is wholly 

 determined in position if the length an* I direction be known 

 of a perpendicular to it 



i the origin ; and this 

 method of fixing a plane 

 leads to one of the most 

 useful forms of its equa- 



. Let OQ be the 

 perpendicular from the 



in to the plane 

 ABC, let p be its length, 

 always considered as 

 positive, and let a, # 7 

 be its direction angles. Let Pa(x, v. ) ho any ]oii 

 16, and draw im o, ( ,rdin.ites 04f, HJT, M /' 1 

 pmjiM ling upon 



} . . :,* 



